Intrinsic Geometric Filtering in Symmetry-Locked Metric-Degenerate Quantum Logic

We introduce \emph{metric-degenerate geometric exchange logic}, where logical operations are organized by controllable degeneracy of an effective interaction metric rather than Hamiltonian time evolution.
The resulting family $\mathrm{Li}$-$\SWAP$ interpolates between $I$ and $\SWAP$ via a degeneracy parameter $\rho$, with half-degenerate gate $\LiHALF=(I+i\SWAP)/\sqrt{2}$.
$\LiHALF$ exhibits a \emph{symmetry-locked invariant manifold}: on $\mathcal{H}_+$ it acts only by a sector-dependent global phase and, in particular, leaves swap-locked product inputs $\ket{\phi\phi}$ product (hence separable).
Under exchange-symmetric noise this yields \emph{geometric filtering}---an extensive zero-entanglement plateau in state-space scans---in stark contrast to conventional controlled gates.
Outside the locked sector, entanglement activates in a controlled manner governed by
$x_{\mathrm{eff}}\equiv\Lambda(\rho)\mathcal{A}(\psi)\mathcal{B}(\phi,\chi)$, showing a one-parameter scaling collapse and a reproducible activation peak.
The framework provides a native instruction set organized by degeneracy phases and symmetry-protected manifolds, fully compatible with no-signaling.